In the \(\overline{\sf MS}\)  scheme the iterative solution for \(a_s(Q^2)\)  is [1]}
\(a_s(Q^2) &=& \frac{1}{\beta _0 L}- \frac{\beta _1}{\beta _0^3 L^2} \ln (L)+ \frac{1}{\beta _0^3 L^3} \Biggl [\frac{\beta _1^2}{\beta _0^2 }(\ln ^2(L) - \ln (L) -1) + \frac{\beta _2}{\beta _0}\Biggr ]\nonumber \\ &&+ \frac{1}{\beta _0^4 L^4} \Biggl [\frac{\beta _1^3}{\beta _0^3 }\Biggl (-\ln ^3(L) + \frac{5}{2} \ln ^2(L) + 2 \ln (L) -\frac{1}{2}\Biggr ) - 3 \frac{\beta _1 \beta _2}{\beta _0^2} \ln (L) + \frac{\beta _3}{2 \beta _0}\Biggr ],\) 
